Contrary to popular belief (about the hierarchy of difficulty levels of the etudes) this etude is very advanced both musically and technically. That bravura part you mention is very difficult even with correct fingering, and for most it will be 2-5, 1-3 fingers throughout . You need precise technique for that section (and all the other sections as well ) to pull off a credible performance of this piece.
I would start off with a sort of "sway" of the hands/arms when going through each set of phrases (down and out..down on the first sixth and the out with the second of the phrase set, sway your arm/wrists/hands thusly) and from there, slowly work your arm and hands to correct positions each sixths , just need to keep practicing that very slowly and really get that feel of how you need to move your arms/hands in the sway like motion and landing precisly on each sixth. Other than that , there really is no other advice , other than just keep working on that slowly and precisly for a long time.
A general note of advice would be for any advanced etude, this set or from any other composer, to bring up to credible playing /performance of it, you really need to let the etude(s) cook under your fingers and mentally for a long while. I mean even years. Sometimes you will have to work on it or something of it, if you cannot overcome a hurdle or there is a ceiling to your technique, put the etude away, work on other things , and then revisit the etude weeks or even months down the road. A constant cooking and rehashing of musical techniques and ideas will somewhat engrain the piece within you.